I thought the kanji for はじめます was:
However, one of my friends tweeted using 初:
Which is correct? Is there a difference in nuance between the two? jisho.org brings up both.
You are confusing the two examples. Both of your examples are correct. Why do you assume as if one in not? Only the first one is read as "はじめます".
You never use
初 to write "はじめます". A close usage I can think of is
初めまして, which is a fixed expression and is not constructive. For writing
はじめます, you always write
始める verb 'start'
初めて adverb/noun 'for the first time'